Algorithmic statistics, prediction and machine learning

Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation. In this paper we extend this framework in two directions. First, the explanations are not only interesting in themselves but also used for prediction: we want to know what kind of data we may reasonably expect in similar situations (repeating the same experiment). We show that some kind of hierarchy can be constructed both in terms of algorithmic statistics and using the notion of a priori probability, and these two approaches turn out to be equivalent. Second, a more realistic approach that goes back to machine learning theory, assumes that we have not a single data string $x$ but some set of "positive examples" $x_1,\ldots,x_l$ that all belong to some unknown set $A$, a property that we want to learn. We want this set $A$ to contain all positive examples and to be as small and simple as possible. We show how algorithmic statistic can be extended to cover this situation.Comment: 22 page

Case Study - IPv6 based building automation solution integration into an IPv4 Network Service Provider infrastructure

The case study presents a case study describing an Internet Protocol (IP) version 6 (v6) introduction to an IPv4 Internet Service Provider (ISP) network infrastructure. The case study driver is an ISP willing to introduce a new “killer” service related to Internet of Things (IoT) style building automation. The provider and cooperation of third party companies specialized in building automation will provide the service. The ISP has to deliver the network access layer and to accommodate the building automation solution traffic throughout its network infrastructure. The third party companies are system integrators and building automation solution vendors. IPv6 is suitable for such solutions due to the following reasons. The operator can’t accommodate large number of IPv4 embedded devices in its current network due to the lack of address space and the fact that many of those will need clear 2 way IP communication channel. The Authors propose a strategy for IPv6 introduction into operator infrastructure based on the current network architecture present service portfolio and several transition mechanisms. The strategy has been applied in laboratory with setup close enough to the current operator’s network. The criterion for a successful experiment is full two-way IPv6 application layer connectivity between the IPv6 server and the IPv6 Internet of Things (IoT) cloud

Destruction of Anderson localization in quantum nonlinear Schr\"odinger lattices

The four-wave interaction in quantum nonlinear Schr\"odinger lattices with disorder is shown to destroy the Anderson localization of waves, giving rise to unlimited spreading of the nonlinear field to large distances. Moreover, the process is not thresholded in the quantum domain, contrary to its "classical" counterpart, and leads to an accelerated spreading of the subdiffusive type, with the dispersion $\langle(\Delta n)^2\rangle \sim t^{1/2}$ for $t\rightarrow+\infty$. The results, presented here, shed new light on the origin of subdiffusion in systems with a broad distribution of relaxation times.Comment: 4 pages, no figure

L\'evy flights on a comb and the plasma staircase

We formulate the problem of confined L\'evy flight on a comb. The comb represents a sawtooth-like potential field $V(x)$, with the asymmetric teeth favoring net transport in a preferred direction. The shape effect is modeled as a power-law dependence $V(x) \propto |\Delta x|^n$ within the sawtooth period, followed by an abrupt drop-off to zero, after which the initial power-law dependence is reset. It is found that the L\'evy flights will be confined in the sense of generalized central limit theorem if (i) the spacing between the teeth is sufficiently broad, and (ii) $n > 4-\mu$, where $\mu$ is the fractal dimension of the flights. In particular, for the Cauchy flights ($\mu = 1$), $n>3$. The study is motivated by recent observations of localization-delocalization of transport avalanches in banded flows in the Tore Supra tokamak and is intended to devise a theory basis to explain the observed phenomenology.Comment: 13 pages; 3 figures; accepted for publication in Physical Review

Localization-delocalization transition on a separatrix system of nonlinear Schrodinger equation with disorder

Localization-delocalization transition in a discrete Anderson nonlinear Schr\"odinger equation with disorder is shown to be a critical phenomenon $-$ similar to a percolation transition on a disordered lattice, with the nonlinearity parameter thought as the control parameter. In vicinity of the critical point the spreading of the wave field is subdiffusive in the limit $t\rightarrow+\infty$. The second moment grows with time as a powerlaw $\propto t^\alpha$, with $\alpha$ exactly 1/3. This critical spreading finds its significance in some connection with the general problem of transport along separatrices of dynamical systems with many degrees of freedom and is mathematically related with a description in terms fractional derivative equations. Above the delocalization point, with the criticality effects stepping aside, we find that the transport is subdiffusive with $\alpha = 2/5$ consistently with the results from previous investigations. A threshold for unlimited spreading is calculated exactly by mapping the transport problem on a Cayley tree.Comment: 6 pages, 1 figur